Is it possible to generate an arbitrary surface, which maps an image onto a point with any distortion we please?

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I'm trying to understand if it's possible to write a function (even a discrete, iterative one) that can generate a surface S, which will take an incoming light field of vectors V, and map it onto a point Q (which is a camera).

This seems possible if we define some initial conditions, but, I'm not sure how to go about it.

A drawing of the problem at hand: enter image description here